The present invention relates to a method of and an apparatus for displaying multidimensional information. More particularly, it relates to a multidimensional information displaying method and a multidimensional information displaying apparatus which are well suited for displaying the results of optimizing computations of optimum control, the optimum design, etc.
As to prior art methods of displaying multidimensional information, there have been contrived a radar chart, facial graph, a constellation graph, etc. (Chernoff's KEIRYO KANRI "(Metering Administration)", Vol. 36, No. 12, pp. 9-12, 1987). Also, a method of displaying multidimensional information afforded as the attribute of a polygonal line has been known from R. M. Pickett, G. G. Grinstein: "Iconographic Displays for Visualizing Multidimensional Data", Proc. IEEE, Int. Conf. Syst. Man. Cybern., pp. 514-519, 1988. With any of these methods, a plurality of information items in which one point or two or more points has/have as its/their attribute can be expressed. With, for example, the facial graph, a plurality of information items concerning one point are quantitatively expressed in terms of the size and inclination of eyes, the profile of a face, etc. by the use of the simplified picture of the face.
Incidentally, the word "multidimensional" is intended to generally mean "of two or more dimensions".
Although each of the prior-art methods of displaying multidimensional information can express a plurality of information items possessed by a finite number of points, it cannot express the situation of the continuous variation of information in a multidimensional space. By way of example, in a case where the incremental or decremental situation of the values of a multivariable function around an arbitrary point in the multidimensional space is to be displayed, it is difficult to directly apply the multidimensional information displaying method in the prior art. For this reason, there has heretofore been adopted a technique wherein the multidimensional space is cut by straight lines or planes containing the arbitrary point, and wherein the situations of the variations of the functional values in the resulting sections are depicted (refer to, for example, the official gazette of Japanese Patent Application Laid-open (KOKAI) No. 273102/1989).
With this technique, however, when the multidimensional space is cut by the planes each being held between two coordinate axes, the number of the planes becomes nC2 where n denotes the number of coordinate axes. For n=100, accordingly, as many as 4950 separate plan views are required, which obstructs a user in intuitively grasping the incremental or decremental situation of the functional values in the multidimensional space.